Multiple Regimes in Northern Hemisphere Height Fields via MixtureModel Clustering*

Abstract

A mixture model is a flexible probability density estimation technique, consisting of a linear combination of k component densities. Such a model is applied to estimate clustering in Northern Hemisphere (NH) 700-mb geopotential height anomalies. A key feature of this approach is its ability to estimate a posterior probability distribution for k, the number of clusters, given the data and the model. The number of clusters that is most likely to fit the data is thus determined objectively. A dataset of 44 winters of NH 700-mb fields is projected onto its two leading empirical orthogonal functions (EOFs) and analyzed using mixtures of Gaussian components. Cross-validated likelihood is used to determine the best value of k, the number of clusters. The posterior probability so determined peaks at k ϭ 3 and thus yields clear evidence for three clusters in the NH 700-mb data. The three-cluster result is found to be robust with respect to variations in data preprocessing and data analysis parameters. The spatial patterns of the three clusters' centroids bear a high degree of qualitative similarity to the three clusters obtained independently by Cheng and Wallace, using hierarchical clustering on 500-mb NH winter data: the Gulf of Alaska ridge, the high over southern Greenland, and the enhanced climatological ridge over the Rockies. Separating the 700-mb data into Pacific (PAC) and Atlantic (ATL) sector maps reveals that the optimal k value is 2 for both the PAC and ATL sectors. The respective clusters consist of Kimoto and Ghil's Pacific-North American (PNA) and reverse PNA regimes, as well as the zonal and blocked phases of the North Atlantic oscillation. The connections between our sectorial and hemispheric results are discussed from the perspective of large-scale atmospheric dynamics.

A mechanistic model of mid-latitude decadal climate variability

“…In both cases, the PDF is strongly skewed, as expected from the shape of the potential V (Fig. 6), thus defining two quasi-stationary states; mixture modeling (Smyth et al 1999) based on the jet position's time series confirms the assertion of two distinct, statistically significant Gaussian components (not shown). Both spectra have a red-noise character and roll off to a white spectrum for frequencies f < 1 year −1 .…”

Ensemble prediction of transitions of the North Atlantic eddy‐driven jet

“…Whilst there have been attempts to explain atmospheric regimes through equilibrium solutions to low-dimensional atmospheric models (Charney and DeVore, 1979;Crommelin, 2003), the link to highdimensional atmospheric global circulation models and the actual atmosphere remains unclear. Regimes in such highdimensional systems are usually diagnosed from output data by examination of probability density function estimates for evidence of multimodality (Silverman, 1981;Corti et al, 1999;Ambaum, 2008;Woollings et al, 2010b) and applying statistical techniques such as clustering (Smyth et al, 1999;Hannachi, 2007;Cassou, 2008;Franzke et al, 2009), rather than by analysis of the dynamical equations themselves.…”

Weather Regime Prediction Using Statistical Learning

“…In spite of these difficulties, agreement on at least a minimal set of weather regimes-extracted from daily, rather than monthly data-has emerged in the community (Cheng and Wallace 1993;Smyth et al 1999). A review of classification methods and results is included, for example, in Ghil and Robertson (2002) and Molteni (2002).…”

“…Using two distinct clustering procedures, these authors obtained four statistically significant weather regimes: the two phases of the North Atlantic Oscillation (NAO ϩ , NAO Ϫ ) and the two phases of a more hemispheric and zonally symmetric mode, which they identified with the Arctic Oscillation (AO ϩ ,A O Ϫ ). They found that these four regimes were in good agreement with previous results (Kimoto and Ghil 1993a,b;Michelangeli et al 1995;Corti et al 1997;Smyth et al 1999). By studying the Markov chain of transitions between regimes, they identified five highly significant transitions that could be organized into two cycles:…”